Non-invasive functional assessment of coronary artery stenosis including simulation of hyperemia by changing resting microvascular resistance

ABSTRACT

A method and system for non-invasive assessment of coronary artery stenosis is disclosed. Patient-specific anatomical measurements of the coronary arteries are extracted from medical image data of a patient acquired during rest state. Patient-specific rest state boundary conditions of a model of coronary circulation representing the coronary arteries are calculated based on the patient-specific anatomical measurements and non-invasive clinical measurements of the patient at rest. Patient-specific rest state boundary conditions of the model of coronary circulation representing the coronary arteries are calculated based on the patient-specific anatomical measurements and non-invasive clinical measurements of the patient at rest. Hyperemic blood flow and pressure across at least one stenosis region of the coronary arteries are simulated using the model of coronary circulation and the patient-specific hyperemic boundary conditions. Fractional flow reserve (FFR) is calculated for the at least one stenosis region based on the simulated hyperemic blood flow and pressure.

This application claims the benefit of U.S. Provisional Application No.61/610,134, filed Mar. 13, 2012, the disclosure of which is hereinincorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates to non-invasive functional assessment ofcoronary artery stenosis, and more particularly, to non-invasivefunctional assessment of coronary artery stenosis from medical imagedata and blood flow simulations.

Cardiovascular disease (CVD) is the leading cause of deaths worldwide.Among various CVDs, coronary artery disease (CAD) accounts for nearlyfifty percent of those deaths. Despite significant improvements inmedical imaging and other diagnostic modalities, the increase inpremature morbidity and mortality for CAD patients is still very high.The current clinical practice for diagnosis and management of coronarystenosis involves the assessment of the diseased vessel either visuallyor by Quantitative Coronary Angiography (QCA). Such assessment providesthe clinician with an anatomical overview of the stenosis segment andparent vessel, including the area reduction, lesion length, and minimallumen diameter, but does not provide a functional assessment of theeffect of the lesion on blood flow through the vessel. Measuring thefractional flow reserve (FFR) by inserting a pressure wire into thestenosed vessel has been shown to be a better option for guidingrevascularization decisions, since the FFR is more effective inidentifying ischemia causing lesions, as compared to invasiveangiography. QCA only evaluates the morphological significance if thestenosis and has a number of other limitations. Pressure wire based FFRmeasurements involve risks associated with the intervention necessary toinsert the pressure wire into the vessel, and for a very narrowstenosis, the pressure wire may induce an additional pressure drop.

BRIEF SUMMARY OF THE INVENTION

The present invention provides a method and system for non-invasivefunctional assessment of coronary artery stenosis. Embodiments of thepresent invention provide a functional assessment of the severity of acoronary artery stenosis by calculating fractional flow reserve (FFR)and/or other functional measurements from medical image data and flowsimulations. Embodiments of the present invention utilize an underlyingreduced-order patient-specific hemodynamic analysis using computationalfluid dynamics (CFD) simulations. This makes it possible to calculateFFR and other hemodynamic quantities characterizing the severity of alesion in near real-time during the image acquisition process, thusallowing for an interactive workflow with a clinician. Embodiments ofthe present invention also utilize other non-image based non-invasivepatient information to calculate boundary conditions forpatient-specific CFD simulations.

In one embodiment of the present invention, patient-specific anatomicalmeasurements of the coronary arteries are extracted from medical imagedata of a patient acquired during rest state. Patient-specific reststate boundary conditions of a model of coronary circulationrepresenting the coronary arteries are calculated based on thepatient-specific anatomical measurements and non-invasive clinicalmeasurements of the patient at rest. Patient-specific hyperemic boundaryconditions of the model of coronary circulation are calculated based onthe rest boundary conditions and a model for simulated hyperemia.Hyperemic blood flow and pressure across at least one stenosis region ofat least one coronary artery are simulated using the model of coronarycirculation and the patient-specific hyperemic boundary conditions.Fractional flow reserve (FFR) of the at least one stenosis region iscalculated based on the simulated hyperemic blood flow and pressure.

In another embodiment of the present invention, Patient-specificanatomical measurements of the coronary arteries from medical image dataof a patient acquired during hyperemia state. Patient-specific hyperemicboundary conditions of a model of coronary circulation representing thecoronary arteries are calculated based on the patient-specificanatomical measurements and non-invasive clinical measurements of thepatient at hyperemia. Hyperemic blood flow and pressure across at leastone stenosis region of at least one coronary artery are simulated usingthe model of coronary circulation and the patient-specific hyperemicboundary conditions. Fractional flow reserve (FFR) of the at least onestenosis region is calculated based on the simulated hyperemic bloodflow and pressure.

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a framework for non-invasive functional assessment ofcoronary artery stenosis according to an embodiment of the presentinvention;

FIG. 2 illustrates a method for non-invasive functional assessment ofcoronary artery stenosis according to an embodiment of the presentinvention;

FIG. 3 illustrates exemplary results for generating a patient-specificanatomical model of the coronary vessel tree;

FIG. 4 illustrates a reduced-order model for simulating coronarycirculation according to an embodiment of the present invention;

FIG. 5 illustrates a method for estimating rest-state microvascularresistance according to an embodiment of the present invention;

FIG. 6 illustrates the calculation of FFR using a personalized reducedorder model according to an embodiment of the present invention; and

FIG. 7 is a high-level block diagram of a computer capable ofimplementing the present invention.

DETAILED DESCRIPTION

The present invention relates to a method and system for non-invasivefunctional assessment of coronary artery stenosis using medical imagedata and blood flow simulations. Embodiments of the present inventionare described herein to give a visual understanding of the methods forsimulating blood flow and assessing coronary artery stenosis. A digitalimage is often composed of digital representations of one or moreobjects (or shapes). The digital representation of an object is oftendescribed herein in terms of identifying and manipulating the objects.Such manipulations are virtual manipulations accomplished in the memoryor other circuitry/hardware of a computer system. Accordingly, is to beunderstood that embodiments of the present invention may be performedwithin a computer system using data stored within the computer system.

FIG. 1 illustrates a framework for non-invasive functional assessment ofcoronary artery stenosis according to an embodiment of the presentinvention. As illustrates in FIG. 1, the framework includes an imageacquisition stage 102, an anatomical modeling stage 104, a blood flowsimulation stage 106, and a fraction flow reserve (FFR) computationphase 108. In the image acquisition stage 102, medical image data, suchas coronary computed tomography (CT), of a patient is acquired, as wellas other non-invasive clinical measurements, such as heart rate, bloodpressure, etc. In the anatomical modeling stage 104, image segmentationand centerline extraction algorithms are used to generatepatient-specific anatomical models of the patient's coronary arteries.The patient-specific anatomical models can be adjusted based on feedbackfrom a clinician 110. In the blood flow simulation stage 106,computational fluid dynamics are used to simulate blood flow through thecoronary arteries. In one embodiment, a reduced-order circulation modelcan be used for patient-specific blood-flow simulations in the vesseltree coupled with a separate model of each stenosis, and the underlyingboundary conditions. Patient-specific boundary conditions are calculatedusing patient-specific modeling of maximal hyperemia conditions and theauto-regulation mechanism. The clinician 110 can provide feedbackregarding the blood flow simulations, for example to change variousparameters of the circulation model or to change the level of modelingof the circulation model. In the FFR computation stage 108, FFR iscalculated for each stenosis based on the simulated pressures resultingfrom the blood flow simulation. The image acquisition stage 102,anatomical modeling stage 104, blood flow simulation stage 106, and FFRcomputation stage 108 are described in greater detail while referring tothe method of FIG. 2

FIG. 2 illustrates a method for non-invasive functional assessment ofcoronary artery stenosis according to an embodiment of the presentinvention. Referring to FIG. 2, at step 202, medical image data andnon-invasive clinical measurements of a patient is received. Medicalimage data from one or multiple imaging modalities can be received. Forexample, the medical image data can include, computed tomography (CT),Dyna CT, magnetic resonance (MR), Angiography, Ultrasound, Single PhotonEmission computed Tomography (SPECT), and any other type of medicalimaging modality. The medical image data can be 2D, 3D or 4D (3D+time)medical image data. The medical image data can be received directly fromone or more image acquisition devices, such as a CT scanner, MR scanner,Angiography scanner, Ultrasound device, etc., or the medical image datamay be received by loading previously stored medical image data for apatient.

In an advantageous embodiment, 3D coronary CT angiography (CTA) imagesare acquired on a CT scanner. The CTA images ensure that the coronaryvasculature, including the vessel(s) that contain the stenosis, isadequately imaged using a contrast agent that is injected into thepatient. At this stage, the clinician may be provided with an option ofidentifying lesions (stenoses) of interest by interactively viewing themon the images. This step can also be performed on the anatomical modelsthat are extracted from the image data (step 204). Alternatively, thestenoses may be automatically detected in the image data using analgorithm for automatic detection of coronary artery stenosis, such asthe method for automatic detection of coronary artery stenosis describedin United States Published Patent Application No. 2011/0224542, which isincorporated herein by reference. In addition to the medical image data,other non-invasive clinical measurements, such as the patient's heartrate and systolic and diastolic blood pressure are also acquired.

At step 204, measurements of the coronary arteries are extracted fromthe medical image data of the patient. In an exemplary embodiment, themedical image data is acquired at rest-state and the measurements of thecoronary arteries are extracted from the image data acquired atrest-state. In an advantageous embodiment, the measurements of thecoronary arteries are extracted by generating a patient-specificanatomical model of the coronary vessel tree is generated from themedical image data, but the present invention is not limited thereto. Inorder to generate the patient-specific anatomical model of the coronaryarteries, the coronary arteries are segmented in the 3D medical imagedata using an automated coronary artery centerline extraction algorithm.The coronary arteries can be segmented using any coronary arterysegmentation method. For example, the coronary arteries can be segmentedin a CT volume using the method described United States Published PatentApplication No. 2010/0067760, which is incorporated herein by reference.Once a coronary artery centerline tree is extracted, cross-sectioncontours can be generated at each point of the centerline tree. Thecross-section contour at each centerline point gives a correspondingcross-section area measurement at that point in the coronary artery. Ageometric surface model is then generated for the segmented coronaryarteries. For example, methods for anatomical modeling of the coronaryarteries are described in U.S. Pat. Nos. 7,860,290 and 7,953,266, bothof which are incorporated herein by reference. In addition to thecoronaries, the patient-specific anatomical model can include the aorticroot together with the proximal part of the aorta. A detailed 3D modelof each stenosis is also extracted using similar algorithms, whichincludes the quantification of the proximal vessel diameter and area,distal vessel diameter and area, minimal lumen diameter and area, andlength of stenosis. FIG. 3 illustrates exemplary results for generatinga patient-specific anatomical model of the coronary vessel tree. Image300 of FIG. 3 shows coronary CTA data. Image 310 shows a centerline tree312 extracted from the CTA data. Image 320 shows a cross-sectioncontours 322 extracted at each point of the centerline tree 312. Image330 shows a 2D surface mesh 332 of the coronary arteries, the aorticroot, and the proximal part of the aorta.

The above described anatomical modeling tasks can be performedautomatically or can be user-driven, thereby allowing the user(clinician) to interactively make changes to the anatomical models toanalyze the effects of such changes on the subsequent computation ofFFR. In addition to the coronary vessel tree, the myocardium is alsosegmented (either automatically or manually) in the medical image datato determine an estimate of the left ventricular mass, which accordingto an embodiment of the present invention, is used to estimate theabsolute resting flow for the patient. In an exemplary embodiment, apatient-specific anatomical model of the heart that is automaticallygenerated from the image data. The anatomical heart model is amulti-component model having multiple cardiac components, including thefour chambers (left ventricle, left atrium, right ventricle, and rightatrium). The anatomical heart model may also include components such asthe heart valves (aortic valve, mitral valve, tricuspid valve, andpulmonary valve) and the aorta. Such a comprehensive model of the heartis used to capture a large variety of morphological, functional, andpathological variations. A modular and hierarchical approach can be usedto reduce anatomical complexity and facilitate an effective and flexibleestimation of individual anatomies. The 4D anatomical heart model can begenerated by generating individual models of each heart component, forexample using marginal space learning (MSL), and then integrating theheart component models by establishing mesh point correspondence.Additional details regarding generation of such a 4D patient-specificheart model are described in United States Published Patent ApplicationNo. 2012/0022843, which is incorporated herein by reference

Returning to FIG. 2, at step 206, a patient-specific blood flowsimulation is performed using boundary conditions calculated based onnon-invasive patient-specific clinical measurements. The hemodynamicquantities of interest for coronary circulation, such as FFR, are basedon average values of flow or pressure over the cardiac cycle. For anefficient clinical workflow for evaluation of FFR via simulations, abalance between model complexity and computation time, withoutcompromising on the accuracy of the results is desirable. In anadvantageous embodiment of the present invention, reduced-order modelsare used for the patient-specific blood flow simulation, which enablesthe assessment of the functional significance of a coronary arterystenosis. The reduced-order models provide accurate estimates of flowand pressure distribution in the vessel tree, and are computationallyefficient, thus enabling a seamless integration with the clinicalworkflow. Although the reduced order model is described herein forcoronary circulation simulation, the present invention is not limitedthereto, and a full-scale model or a multi-scale model can be used aswell.

FIG. 4 illustrates a reduced-order model for simulating coronarycirculation according to an embodiment of the present invention. Asshown in FIG. 4, a heart model 402 is coupled at the root of the aorta.The heart model 402 may be implemented as a full 3D heart model or maybe implemented as a lumped model parameterized through patient-specificdata. The aorta and the large arteries (e.g., the left coronary artery(LCA), right coronary artery (RCA), etc.) are represented as 1D bloodflow models 404, 406, 408, 410, 412, 414, 416, 418, and 420 since these1D blood flow models 404-418 produce reliable results in terms ofpressure and flow rate values and take into account wave propagationphenomena. All microvascular beds will be simulated through lumpedparameter models 422, 424, 426, 428, and 430 which account for theresistance applied to the blood flow and for the compliance of thedistal vessels. For the coronary arterial tree, the flow in the large(epicardial) vessels is computed through 1D models in a systemic treemodel 421. The stenosis segments 432 and 434 (i.e., areas in the vesselswere stenosis or narrowing is detected) cannot be simulated using the 1Dblood flow models since there is a high variation in cross-sectionalarea and the shape of the stenosis influences the blood flow behaviorand especially the trans-stenotic pressure drop which plays a major rolein the assessment of the functional importance of such a stenosis. Thecoronary vascular bed is modeled through lumped parameter models 424,426, 428, and 430, which are adapted to the coronary circulation in thesense that they take into account the effects of the myocardialcontraction on the flow waveform.

Reduced-Order Model of Coronary Circulation

As shown in FIG. 4, the aorta (404), the large arteries supplied by theaorta (406, 408, 410, 412, 414, 416, 418, and 420), and the coronaryepicardial vessels (421) are modeled as axi-symmetric 1-D vesselsegments, where the blood-flow satisfies the following properties:conservation of mass, conservation of momentum, and a state equation forwall deformation. The vessel wall can modeled as a purely elastic orvisco-elastic. The inlet boundary condition can be prescribed through animplicit coupling with the heart model 402, or through measured flowdata. The outlet boundary condition is given by the implicit couplingwith the models of the coronary vascular beds (424, 426, 428, and 430),while the junctions (bifurcations) are solved by considering thecontinuity of total pressure and flow. Additionally, the following losscoefficients may be introduced which account for the energy loss at thejunctions, which depend on the angles between the vessel segments:

$\begin{matrix}{{\frac{\partial{A(t)}}{\partial t} + \frac{\partial{q(t)}}{\partial x}} = 0} & (1) \\{{\frac{\partial{q(t)}}{\partial t} + {\frac{\partial}{\partial t}\left( {\alpha\;\frac{q^{2}(t)}{A(t)}} \right)} + {\frac{A(t)}{\rho}\frac{\partial{p(t)}}{\partial x}}} = {K_{R}\frac{q(t)}{A(t)}}} & (2) \\{{{p(t)} = {\frac{4}{3}\frac{Eh}{r_{0}}\left( {1 - \sqrt{\frac{A_{0}}{A(t)}}} \right)}},} & (3)\end{matrix}$where q is the flow rate, A is the cross-sectional area, p is thepressure, α is the momentum-flux correction coefficient, K_(R) is afriction parameters, ρ is the density, E is the Young modulus, h is thewall thickness and r₀ is the initial radius. The wall properties may bedetermined through an empirical relationship fit to the measured data inthe extracted patient-specific anatomical model or based onpatient-specific estimations of the wall compliance. Other alternativeformulations of the quasi-1-D flow equations can also be used, modelingthe effects of visco-elasticity, non-Newtonian behavior, etc.Stenosis Model

The above quasi 1-D equations (Equations 1-3) are derived by consideringa series of simplifying assumptions which all hold well for normal,healthy vessels. One of the assumptions is that the axial velocity isdominant and the radial components are negligible. This assumption nolonger holds in case of sudden changes in lumen diameter, e.g. for astenosis, and the radial components can no longer be excluded. Hence,the quasi 1-D equations do not correctly capture the pressure dropacross the stenosis.

In terms of previous research activities, much attention has beendirected towards the local velocity fields, but for the FFR assessmentonly the trans-stenotic pressure drop is important. In an advantageousimplementation, semi-empirical stenosis models can be included in the1-D blood flow models, which obtain accurate results as compared to fullscale models. For example, in the model below, the pressure drop isexpressed as a sum of three terms (viscous term, turbulent or Bernoulliterm, and inertance term):

$\begin{matrix}{{{\Delta\; P_{s}} = {{\frac{\mu\; K_{v}}{2\pi\; r_{0}^{3}}q} + {\frac{\rho\; K_{t}}{2A_{0}^{2}}\left( {\frac{A_{0}}{A_{s}} - 1} \right)^{2}{q}q} + {\frac{\rho\; K_{u}L_{s}}{A_{0}}\frac{\partial q}{\partial t}}}},} & (4)\end{matrix}$where μ is the blood viscosity, L_(s) is the stenosis length, K_(v),K_(t) and K_(u) are the viscous, turbulent, and inertance coefficients,respectively (all the quantities indexed with 0 refer to the normaldimensions while the quantities indexed with s refer to the stenosedvalues). In an advantageous embodiment, such a semi-empirical model foreach stenosis segment (432 and 434) is coupled with the vessel tree (andthe underlying heart and coronary bed models) to compute thephysiological pressure drop across the stenosis, both during rest stateand at maximal hyperemia. It is to be understood that the presentinvention is not limited to the semi-empirical stenosis model ofEquation (4), and other such models of the stenosis, with multiplepressure drop factors, may be used alternatively. Additionally, in analternative implementation, a full-order 3D model of each stenosis maybe coupled with the rest of the vessel tree to simulate the pressuredrop across the stenosis. In this case, the patient-specific 3Dgeometric model of the stenosis extracted from the medical image data(e.g., CTA data) is used in conjunction with quantitative coronaryangiography (QCA)-like measures to personalize the stenosis model forthe individual patient.

Regarding coupling of the reduced-order or full-order stenosis model tothe rest of the coronary vessel tree, in a first possibleimplementation, the momentum equation is adapted and the additionalpressure drop determined by the turbulent term is included on the righthand side of the equation as an additional loss term. In a secondpossible implementation, the regular momentum equation is disregardedcompletely and replaced by Equation (2). The segments treated asstenosis segments are coupled to the regular segments of the coronaryvessel tree by considering continuity of total pressure and flow rate.

Patient-Specific Modeling of Coronary Bed Boundary Conditions

An important aspect of the flow simulations is represented by theboundary conditions at the termination of the coronary vessel tree(outflow boundary conditions). Generally, pressure, flow, or arelationship between flow and pressure may be imposed at the terminalsites of the arterial vessel tree. If measured data, e.g. time-varyingvelocity, flow rate, or even pressure, are available, they can bereadily applied. In the absence of such information (which is typicallythe case), embodiments of the present invention calculate specialboundary conditions that model the behavior of the distal arterialsegments. Hence, the microvascular beds are modeled through lumped orO-D models: the systemic beds can represented by regular windkesselelements containing varying number of elements (for example, between twoand four elements), while coronary beds are represented by specialmodels which account for the influence of the myocardial contraction onthe flow waveform (low during systole and high during early diastole).FIG. 4 displays an example of such specialized models for the coronarycirculation and presents the detailed elements of this type of boundarycondition.

The main characteristic of such lumped models is that the myocardialcontraction is taken into account by introducing the left or rightventricular pressure, depending on the location of the coronary tree onthe heart. The model displayed in FIG. 4 treats the microvascular bed asa single unit, but it is also possible to utilize more specializedmodels which consider separately the contribution of the subepicardialand subendocardial microvascular beds. Generally, subepicardial vesselsare less affected by heart contraction (they represent the outer layersof the myocardium), while subendocardial vessels are more affected bythe action of the outer (they represent the inner layers, closer to theheart chambers). This is the main reason why subendocardial are moreprone to ischemia and to myocardial infarction.

Since the resistance values of the large vessels are very small comparedto the resistances of the arterioles and capillaries, the overallpressure levels are almost solely determined by the microvascular beds.In the context of non-invasive FFR evaluation, the microvascular beds ingeneral, and the coronary beds in particular play another major role.Since FFR is based on values determined at hyperemia, in order tonon-invasively determine the value of this diagnostic indicator, theblood flow simulation has to model the hyperemic state. In clinicalpractice, FFR is measured after the intravenous or intracoronaryadministration of a vasodilator. In case of multi-vessel disease orserial stenosis it is important to have an increased duration of thehyperemic state in order to evaluate the functional significance of allstenosis and to generate reliable pull-back curves. Hence, oftenintravenous administration of the vasodilator is preferred. This leadsto a slight increase of heart rate and decrease of blood pressure. Sincefor a simulation the effect of an intracoronary vasodilator can beextended indefinitely, and this alternative to obtain hyperemia does notinfluence heart rate and blood pressure, thus being easier to model,this approach is desirable. However, although the intravenousadministration can be simulated, all microvascular beds have to beadapted accordingly.

The administration of hyperemia inducing drugs (adenosine, papaverineetc.) leads to a vasodilation effect of the microvascular beds, whichrepresents an important decrease of the resistance values. Theresistance values inside the systemic or coronary lumped models (for thenormal state) may be obtained from patient-specific measurements, fromliterature data, or from the non-linear relationship between resistancesand lumen size. Compliances play a secondary role since they onlyinfluence the transient values and not the average pressures which areof interest for the evaluation of FFR. The coronary hyperemic state ismodeled through a corresponding decrease in the microvascularresistances, as caused by the administration of intracoronary adenosine(it has been shown that the epicardial, i.e. large arteries are notinfluenced by the vasodilator) and leads to a three to five-foldincrease of normal coronary flow in healthy vessels. Coronaryauto-regulation protects the myocardium against ischemia during reststate and leads to decreased resistances for the diseased vessel, thereference value being the flow which has to be identical to thenoon-diseased case. The normal state can thus be easily modeled but doesnot represent a very high interest for the evaluation of FFR.

The main parameters which have to be estimated are the mean arterialpressure (MAP) and the coronary microvascular resistances (theresistances of the proximal epicardial arteries are negligible comparedto the microvascular resistances). Since FFR uses only average measuresof pressures (distal and proximal to the stenosis), compliances need notbe estimated accurately because they only influence the waveform ofpressure and flow, but not the average values, which are only determinedby the resistances. MAP can be easily measured non-invasively and asstated previously is similar at both rest and hyperemia state. Coronarymicrovascular resistances on the other hand are much lower at hyperemiain order to allow for an increased flow rate. To determine theresistance values at hyperemia, first, the rest resistances can beestimated and then the effect of the administration of a vasodilationdrug can be estimated and the hyperemia resistances can be estimated.

According to an advantageous embodiment of the present invention, thecalculation of patient-specific boundary conditions for the coronary bedis implemented in two stages: in the first stage, the mean arterialpressure (MAP) and the coronary microvascular resistance at each outletof the patient-specific vessel tree during a simulated rest-state areestimated, and in the second stage, the microvascular resistances athyperemia are estimated.

FIG. 5 illustrates a method for estimating rest-state microvascularresistance according to an embodiment of the present invention. Asillustrates in FIG. 5, at step 502, mean arterial pressure (MAP) isestimated based on the patient's heart rate, systolic blood pressure,diastolic blood pressure. In particular, the MAP is calculated asMAP=DBP+[⅓+(HR·0.0012)]·(SBP−DBP)  (5)where HR, SBP, and DBP denote the patient's heart rate, systolic bloodpressure, diastolic blood pressure, respectively, which are measurenon-invasively.

At step 504, the total myocardial perfusion q_(rest) is estimated usingthe rate-pressure product (RPP) relationship. The RPP is the product ofthe heart rate and the systolic blood pressure. Starting from the RPP,the resting perfusion q_(rest) can be estimated as:q _(rest)=8·{[0.7·(HR·SBP)·10⁻³]−0.4} [ml/min/100 g],  (6)where HR is the heart rate and SBP is the systolic blood pressure. Itcan be noted that this relationship is only valid if the flow meets theoxygen demand of the subject.

At step 506, the total resting coronary flow is estimated based on theresting perfusion q_(rest) and the mass of the patient's left ventricle(LV). The mass of the left ventricle is estimated based on quantitiesderived from segmentation of the medical image data. In one possibleimplementation, the myocardium is segmented using automatic heartchamber segmentation, for example using a MSL machine-learning basedmethod. The volume can be automatically calculated from the segmentedmyocardium, for example using the method described in U.S. Pat. No.8,098,918, entitled “Method and System for Measuring Left VentricleVolume”, which is incorporated herein by reference. The LV volume isthen multiplied by the density to provide the mass of the LV (M_(LV)).

In another possible implementation. the volume of the LV chamber can bedetermined as:

$\begin{matrix}{{V = {\frac{4}{3} \cdot \pi \cdot \frac{d_{a}}{2} \cdot \frac{d_{l}}{2} \cdot {\frac{l}{2}\lbrack{ml}\rbrack}}},} & (7)\end{matrix}$where d_(a) and d_(l) are two transverse diameters calculated from twoperpendicular planes, and/is the maximum chamber length measured on oneof the perpendicular planes. The calculated volume is then corrected bya known regression equations:V′=0.928·V−3.8 [ml].  (8)After measuring the wall thickness, the volume of the LV chambertogether with the muscle wall can be calculated as follows:

$\begin{matrix}{V_{c + w} = {\frac{4}{3} \cdot \pi \cdot \left( {\frac{d_{a}}{2} + h} \right) \cdot \left( {\frac{d_{l}}{2} + h} \right) \cdot {{\left( {\frac{l}{2} + h} \right)\lbrack{ml}\rbrack}.}}} & (9)\end{matrix}$The LV mass can then be calculated as:M _(LV)=(V _(c+w) −V′)·1.050 [kg],  (10)where 1.050 represents the specific gravity of the heart muscle.

In another possible implementation, the LV mass can be calculated as:M _(LV)=1.04·[(LVEDD+IVSEDD+PWEDD)³−LVEDD³]−13.6,  (11)where LVEDD is the left ventricular end-diastolic volume, IVSEDD is theintra-ventricular septum end-diastolic diameter, and PWEDD is theposterior wall end-diastolic diameter.

In order to determine the absolute value of the resting flow, theresting perfusion has to be multiplied by the myocardial mass. In normalhearts, it is generally assumed that the left ventricle represents twothirds of the total mass, while the right ventricle and atria representthe other third. Accordingly, once the left ventricular mass M_(LV) isdetermined, the absolute resting flow can be determined as:Q _(rest) =q _(rest)·1.5·M _(LV) [ml/min].  (12).Having determined that the flow rate is proportional to the cube of theradius, absolute resting flow, which is the sum of all outflow flows ofthe coronary vessels may be expressed as:

$\begin{matrix}{Q_{rest} = {{\sum\limits_{i = 1}^{n}{k \cdot r_{i}^{3}}} = {\sum\limits_{i = 1}^{n}{Q_{i}.}}}} & (13)\end{matrix}$

At step 508, the terminal resistance for each vessel is calculated. Inparticular, the terminal resistance is calculated using the followingrelationship:

$\begin{matrix}{R_{i} = {\frac{MAP}{Q_{i}}.}} & (14)\end{matrix}$Q_(i) is determined by:

$\begin{matrix}{{\frac{Q_{i}}{Q_{rest}} = {\frac{k \cdot r_{i}^{3}}{\sum\limits_{j = 1}^{n}{k \cdot r_{j}^{3}}} = \frac{r_{i}^{3}}{\sum\limits_{j = 1}^{n}r_{j}^{3}}}},} & (15)\end{matrix}$and hence:

$\begin{matrix}{{Q_{i} = \frac{Q_{rest} \cdot r_{i}^{3}}{\sum\limits_{j = 1}^{n}r_{j}^{3}}},} & (16)\end{matrix}$where r_(i) is the terminal radius of a vessel (equal to half of theterminal diameter d_(i)) and n is a power coefficient. Thus, theterminal resistance at each vessel can be calculated as:

$\begin{matrix}{R_{i} = {\frac{MAP}{Q_{i}} = {\frac{{MAP} \cdot {\sum\limits_{j = 1}^{n}r_{j}^{3}}}{Q_{rest} \cdot r_{i}^{3}}.}}} & (17)\end{matrix}$

The second stage of estimating the patient-specific coronary bedboundary conditions calculates hyperemic-state microvascularresistances. The input to the second stage is represented by the restmicrovascular resistances calculated using Equations (5)-(17), asdescribed in the method of FIG. 5. The coronary hyperemic state can bemodeled by decreasing the microvascular resistances, which is caused bythe administration of intracoronary adenosine. It has been shown thatthe epicardial arteries are not influenced by the vasodilator, thus onlythe microvascular resistance needs to be changed. This ultimately leadsto a three to five-fold increase of coronary flow in healthy vessels.Adenosine leads to an increase in coronary flow velocity of around 4.5for normal, healthy subjects (with no coronary artery disease). Thecoronary flow velocity reserve (CFVR) value is determined after theadministration of intracoronary boluses, intracoronary infusions, orintravenous infusions to a series of subjects. The value of 4.5 isconfirmed in all three sets of experiments. The increase in coronaryvelocity is equal to an increase in flow, since a similar velocityprofile can be assumed for both rest and hyperemic state. Since duringhyperemia, blood pressure decreases slightly, a 4.5-fold increase inflow does not mean a 4.5-fold decrease in coronary resistance. A totalcoronary resistance index (TCRI) can be computed as described below.

The hyperemic microvascular resistances can be calculated as follows.First, the resting average peak velocity is calculated based on thepatient's heart rate and systolic blood pressure as:rAPV=0.0009·SBP·HR+5.925 [cm/s],  (18)where the rate-pressure product is expressed in [mmHg*beats/min]. CFVRvalues can then be calculated for each mean branch of the coronaryvessel tree using the following equations:LAD: CFVR=10^(1.16−0.48·log(rAPV)−0.0025·age)  (19)LCX: CFVR=10^(1.14−0.45·log(rAPV)−0.0031·age)  (20)RCA: CFVR=10^(1.15−0.50·log(rAPV)−0.0021·age).  (21)

The TCRI can then be calculated using a value of 5 mmHg for ΔMAP:

$\begin{matrix}{\frac{1}{TCRI} = {\frac{\frac{{MAP}_{rest}}{Q_{rest}}}{\frac{{MAP}_{hyper}}{Q_{hyper}}} = {{\frac{{MAP}_{rest}}{{MAP}_{hyper}} \cdot \frac{Q_{hyper}}{Q_{rest}}} = {{\frac{{MAP}_{rest}}{{MAP}_{hyper}} \cdot {CFVR}} = {\frac{{MAP}_{rest}}{{MAP}_{rest} - {\Delta\;{MAP}}} \cdot {{CFVR}.}}}}}} & (22)\end{matrix}$Alternatively, instead of the above described steps, the followingrelationship may be used to determine the TCRI value, based onexperimental results having a very low standard deviation and thus highreliability:

$\begin{matrix}{{TCRI} = \left\{ \begin{matrix}{{{0.0016 \cdot {HR}} + {0.1\mspace{14mu}{for}\mspace{14mu}{HR}}} \leq {100\mspace{14mu}{bpm}}} \\{{{0.001 \cdot {HR}} + {0.16\mspace{14mu}{for}\mspace{14mu}{HR}}} > {100\mspace{14mu}{{bpm}.}}}\end{matrix} \right.} & (23)\end{matrix}$

The hyperemic microvascular resistances are then calculated based on theresting-state microvascular resistances, using the following equation:(R _(i))_(hyper)=(R _(i))_(rest)·TCRI,  (24)where (R_(i))_(rest) is the value for the resting-state microvascularresistance determined using the method of FIG. 6, described above. It isto be understood that alternative methods for estimating themicrovascular resistance at hyperemia can also be readily incorporatedinto the method for calculating FFR described herein.Heart Model

The intra-myocardial pressure is an important element of the coronarymodeling. Hence, a major component of the reduced-order modeling is theheart model. FIG. 4 displays a lumped heart model 402 but also moresophisticated or complete models may be used. There are several lumpedmodels, such as the varying elastance model and the single fiber model.These can determine the pressure and the flow in the different heartchambers without considering a spatial model of the heart. Severalparameters like contractility, stroke volume, time-to-maximum, deadvolume (V₀), heart rate can be adapted in order to account for differentstates of the body and to personalize the model. The simplest model isrepresented by the varying elastance model which can readily be coupledto the aortic input through a lumped aortic valve model 402 andindirectly coupled to the specialized microvascular models of thecoronary arterial tree through the left ventricular pressure. Thevarying elastance model can be expressed as:

$\begin{matrix}{{E(t)} = {\frac{P_{LV}(t)}{{V_{LV}(t)} - V_{0}}.}} & (25)\end{matrix}$

Several considerations have lead to the modeling of all major arteriesof the systemic tree and not only of the coronary arterial tree. Thisway the heart can be directly coupled to the aorta and the flow isdetermined by the interaction between the left ventricle and the systemimpedance. Also, the overall pressure level is mainly determined by thelarge arteries, while the coronary resistances (microvascular andstenosis-based) have a negligible influence and hence the trans-stenoticpressure drops may be modeled more precisely. Depending on theadditional data available (such as echocardiography, Cardiac MRI), theheart models can be further personalized for an individual patient.These modalities allow for information such as stroke volume, ejectionfraction etc, which can readily be used to personalize the heart model.

Returning to FIG. 2, at step 208, FFR is calculated for each stenosisbased on the blood flow simulations. Once the time-varying pressure andflow rates are computed from the patient-specific reduced-ordersimulations at maximal vasodilation, the FFR value is determined bysimply taking the ratio of the mean pressure distal to the stenosis(P_(d)) with respect to the mean aortic pressure (P_(a)) during thecardiac cycle:

$\begin{matrix}{{FFR} = {\frac{P_{d}}{P_{a}}.}} & (26)\end{matrix}$This calculation can be performed automatically for all the lesions thatthe user specified during the anatomic modeling step. Additionally, theuser can also specify any location in the vessel tree during apost-processing step, and the corresponding FFR value will then becomputed as described above.

FIG. 6 illustrates the calculation of FFR using a personalized reducedorder model according to an embodiment of the present invention. Asshown in FIG. 6, at 602, the effect of the adrenosine on the terminalresting-state microvascular resistances is estimated, resulting in theterminal hyperemia microvascular resistances. At 604, the reduce ordersimulation is performed using the heart model, coronary vessel geometry,estimates resistances at hyperemia, and the stenosis model. Thesimulation simulates the hyperemic blood flow and hyperemic pressure. At606, FFR is calculated as a ratio of the simulated mean hyperemicpressure distal to the stenosis (P_(d)) and the mean hyperemic aorticpressure (P_(a)) over a cardiac cycle. In addition to FFR, otherhemodynamic quantities based on the flow rates and pressure can also becalculated from the results of the blood flow simulations.

In addition to Coronary CT data, the above method can also be applied onother image data, such as 3-D Angio, Rotational Angiography, Dyna-CT.For angiographic data, the image based analysis of the propagation ofthe contrast agent, via a spatio-temporal representation of contrastpropagation can be used to robustly recover the flow rate over time,both during resting and maximal hyperemia. At the same time, such imageacquisition can also be carried out during maximal hyperemia condition,and used in conjunction with the empirical stenosis model to determinethe FFR value. Accordingly, in an alternative embodiment of the presentinvention, the medical image data can be acquired at hyperemia, and thehyperemia boundary conditions detected directly based on the image dataand non-invasive non-imaging measures (e.g., heart rate, systolic bloodpressure, and diastolic blood pressure) acquired at hyperemia. Thesimulations using the hyperemia boundary conditions can then be used tocalculate FFR.

Other sources of patient information (when present) can be used forfurther personalization of the models. For example, echocardiography canprovide 3-D strain maps, which may be used to model the influence of theheart contractions on each of the epicardial coronary vessels. There isa major difference between the right and left side of the heart but alsolocally more detailed variations can be taken into account. A 3-D strainmap extracted from the image data may be used for imposing additionalpatient-specific boundary conditions. Along the same lines, 3-D colorflow or Phase Contrast MRI measurements can also be used to provideinlet flow boundary conditions for the coronary vessel tree. Theavailability of 3-D+t anatomical models of the heart (from CT, MR orUltrasound data) makes it possible to simulate the blood flow in theheart chambers by CFD. This can also be used to further personalize themodels and impose the boundary conditions.

Since the FFR values are computed in near real-time using thereduced-order simulation model, a clinician can provide feedback toobserve the effects of various changes, such as variability due tochanges in the segmentation result, variability due to changes in theseed point for centerline extraction and missing centerlines,variability due to changes in locations of branch terminations and theeffect on the boundary conditions, variability due to side vessel branchelimination, and variability due to overall image quality.

Instead of using the rate-pressure product in order to determinecoronary perfusion, as described above, in an alternative implementationit is possible to use the stress-mass-rate product in order to determinedirectly the global coronary flow:

$\begin{matrix}{{Stress} = {\frac{0.334 \cdot {SBP} \cdot {LVDd}}{LVPWT} \cdot \left( {1 + \frac{LVPWT}{LVDd}} \right)}} & (27)\end{matrix}$where SBP is systolic blood pressure, LVDd is left ventricle diameter atend-diastole and LVPWT is left ventricular posterior wall thickness. Theglobal coronary resting flow can then be determined as follows:Q _(rest)=0.0218·Stress·M _(LV)·HR·10⁻³+120.11,  (28)where the stress-mass-rate product is expressed in[g*kdyne/cm2*beats/min] and MLV represents the left ventricular mass.

The above-described methods for non-invasive assessment of coronaryartery stenosis may be implemented on a computer using well-knowncomputer processors, memory units, storage devices, computer software,and other components. A high-level block diagram of such a computer isillustrated in FIG. 7. Computer 702 contains a processor 704, whichcontrols the overall operation of the computer 702 by executing computerprogram instructions which define such operation. The computer programinstructions may be stored in a storage device 712 (e.g., magnetic disk)and loaded into memory 710 when execution of the computer programinstructions is desired. Thus, the steps of the methods of FIG. 2 may bedefined by the computer program instructions stored in the memory 710and/or storage 712 and controlled by the processor 704 executing thecomputer program instructions. An image acquisition device 720, such asa CT scanning device, MR scanning device, Ultrasound device, etc., canbe connected to the computer 702 to input image data to the computer702. It is possible to implement the image acquisition device 720 andthe computer 702 as one device. It is also possible that the imageacquisition device 720 and the computer 702 communicate wirelesslythrough a network. The computer 702 also includes one or more networkinterfaces 706 for communicating with other devices via a network. Thecomputer 702 also includes other input/output devices 708 that enableuser interaction with the computer 702 (e.g., display, keyboard, mouse,speakers, buttons, etc.). Such input/output devices 708 may be used inconjunction with a set of computer programs as an annotation tool toannotate volumes received from the image acquisition device 720. Oneskilled in the art will recognize that an implementation of an actualcomputer could contain other components as well, and that FIG. 7 is ahigh level representation of some of the components of such a computerfor illustrative purposes.

The foregoing Detailed Description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the invention disclosed herein is not to be determined from theDetailed Description, but rather from the claims as interpretedaccording to the full breadth permitted by the patent laws. It is to beunderstood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that variousmodifications may be implemented by those skilled in the art withoutdeparting from the scope and spirit of the invention. Those skilled inthe art could implement various other feature combinations withoutdeparting from the scope and spirit of the invention.

The invention claimed is:
 1. A method for non-invasive assessment ofcoronary artery stenosis, comprising: extracting patient-specificanatomical measurements of the coronary arteries from medical image dataof a patient acquired during a rest state; automatically detecting atleast one stenosis region in at least one coronary artery from themedical image data; calculating by a processor patient-specific reststate boundary conditions of a model of coronary circulationrepresenting the coronary arteries using the patient-specific anatomicalmeasurements and non-invasive clinical measurements of the patient atrest, wherein calculating the patient-specific rest state boundaryconditions comprises calculating a resting microvascular resistance at atermination of each of a plurality of branches of the coronary arteriesusing the patient-specific anatomical measurements and the non-invasiveclinical measurements of the patient at rest; calculating by a processorpatient-specific hyperemic boundary conditions of the model of coronarycirculation using the rest boundary conditions and a model for simulatedhyperemia, wherein the model for simulated hyperemia simulates hyperemiain the patient by changing only the resting microvascular resistance ata termination of each of a plurality of branches of the coronaryarteries to a hyperemic microvascular resistance calculated as afunction of the resting microvascular resistance at the termination ofeach of the plurality of branches without changing blood pressure orheart rate boundary conditions, and wherein calculating thepatient-specific hyperemic boundary conditions comprises calculating thehyperemic microvascular resistance at the termination of each of theplurality of branches using the calculated resting microvascularresistance by: calculating a resting average peak velocity as a functionof a measured heart rate and a measured systolic blood pressure of thepatient, calculating a coronary flow velocity reserve (CFVR) value foreach branch of the coronary arteries as a function of the restingaverage peak velocity and an age of the patient, calculating apatient-specific total coronary resistance index (TCRI) as a function ofthe CFVR value and an estimated resting mean arterial pressure (MAP),and calculating the hyperemic microvascular resistance at thetermination of each of the plurality of branches as a function of thecalculated resting microvascular resistance and the patient-specificTCRI; simulating by a processor hyperemic blood flow and pressure acrossthe at least one automatically detected stenosis region of the at leastone coronary artery using the model of coronary circulation and thepatient-specific hyperemic boundary conditions, wherein the model ofcoronary circulation comprises a reduced order stenosis pressure dropmodel representing the at least one stenosis region and the reducedorder stenosis pressure drop model calculates a pressure drop across theat least one stenosis region as a sum of a viscous term, a turbulentterm, and an inertance term:${{\Delta\; P_{s}} = {{\frac{\mu\; K_{v}}{2\;\pi\; r_{0}^{3}}q} + {\frac{\rho\; K_{t}}{2A_{0}^{2}}\left( {\frac{A_{0}}{A_{s}} - 1} \right)^{2}{q}q} + {\frac{\rho\; K_{u}L_{s}}{A_{0}}\frac{\partial q}{\partial t}}}},$where μ is blood viscosity, L_(s) is a length of the at least onestenosis region, q is a flow rate, A_(s) is a cross-sectional area ofthe at least one stenosis region, A₀ is a cross-sectional area of anon-stenosis region in the at least one coronary artery, ρ is a blooddensity, r₀ is a radius of the non-stenosis region in the at least onecoronary artery, and K_(v), K_(t) and K_(u) are viscous, turbulent, andinertance coefficients, respectively; and calculating by a processorfractional flow reserve (FFR) of the at least one stenosis region usingthe simulated hyperemic blood flow and pressure.
 2. The method of claim1, wherein the coronary circulation model comprises one-dimensionalcomputational models representing the coronary arteries and aorta of thepatient.
 3. The method of claim 2, wherein the reduced order stenosispressure drop model representing the at least one stenosis region iscoupled to the one-dimensional computational model representing the atleast one coronary artery.
 4. The method of claim 3, wherein the reducedorder stenosis pressure drop model representing the at least onestenosis region is coupled to the one-dimensional computational modelrepresenting the at least one coronary artery using a momentum equationthat includes a pressure drop determined by the turbulent term as a lossterm.
 5. The method of claim 1, wherein calculating the restingmicrovascular resistance at the termination of each of the plurality ofbranches using the patient-specific anatomical measurements and thenon-invasive clinical measurements of the patient at rest comprises:calculating the mean arterial pressure (MAP) as a function of themeasured heart rate, the measured systolic blood pressure, and ameasured diastolic blood pressure of the patient; calculating a totalresting coronary flow as a function of a product of an estimated stressvalue, a mass of a left ventricle of the patient, and the measured heartrate; and calculating the resting microvascular resistance at thetermination of each of the plurality of branches as a function of theMAP and the total resting coronary flow.
 6. The method of claim 5,wherein calculating a total resting coronary flow as a function of aproduct of an estimated stress value, a mass of a left ventricle of thepatient, and the measured heart rate comprises: calculating theestimated stress value as a function of the measured systolic bloodpressure, a diameter of the left ventricle of the patient atend-diastole, and a posterior wall thickness of the left ventricle. 7.The method of claim 5, wherein calculating a total resting coronary flowas a function of a product of an estimated stress value, a mass of aleft ventricle of the patient, and the measured heart rate comprises:calculating the estimated stress value as${{Stress} = {\frac{0.334 \cdot {SBP} \cdot {LVDd}}{LVPWT} \cdot \left( {1 + \frac{LVPWT}{LVDd}} \right)}},$where SBP is the measured systolic blood pressure, LVDd is a diameter ofthe left ventricle of the patient at end-diastole, and LVPWT is aposterior wall thickness of the left ventricle of the patient; andcalculating the total resting coronary flow asQ _(rest)=0.0218·Stress·M _(LV)·HR·10⁻³+120.11, where M_(LV) is the massof the left ventricle of the patient and HR is the measured heart rate.8. The method of claim 1, wherein calculating a resting average peakvelocity as a function of a measured heart rate and a measured systolicblood pressure of the patient comprises: calculating the resting averagepeak velocity as rAPV=0.0009·SBP·HR+5.925 where SBP is the measuresystolic blood pressure and HR is the measure heart rate.
 9. The methodof claim 1, wherein calculating a patient-specific total coronaryresistance index (TCRI) as a function of the CFVR value and an estimatedresting mean arterial pressure (MAP) comprises: calculating thepatient-specific${{TCRI}\mspace{14mu}{as}\mspace{14mu}\frac{1}{TCRI}} = {\frac{{MAP}_{rest}}{{MAP}_{rest} - {\Delta\;{MAP}}}.}$CFVR, wherein MAP_(rest) is the estimated resting mean MAP and ΔMAP is apredetermined constant value.
 10. The method of claim 1, whereincalculating the hyperemic microvascular resistance at the termination ofeach of the plurality of branches as a function of the calculatedresting microvascular resistance and the patient-specific TCRIcomprises: calculating the hyperemic microvascular resistance at thetermination of each of the plurality of branches as a product of thecalculated resting microvascular resistance and the patient-specificTCRI.
 11. The method of claim 2, wherein the coronary circulation modelfurther comprises lumped models representing coronary microvascularbeds, each coupled to a termination of a one-dimensional computationalmodel representing a coronary artery branch.
 12. The method of claim 1,wherein calculating the resting microvascular resistance at thetermination of each of the plurality of branches using thepatient-specific anatomical measurements and the non-invasive clinicalmeasurements of the patient at rest comprises: calculating the meanarterial pressure (MAP) as a function of the measured heart rate, themeasured systolic blood pressure, and a measured diastolic bloodpressure of the patient; calculating a resting myocardial perfusion as afunction of a rate-pressure product that is a product of the measuredheart rate and the measured systolic blood pressure of the patient;calculating a total resting coronary flow as a function of thecalculated resting myocardial perfusion and a mass of a left ventricleof the patient; and calculating the resting microvascular resistance atthe termination of each of the plurality of branches as a function ofthe MAP and the total resting coronary flow.
 13. The method of claim 12,wherein the mass of the left ventricle is estimated from the medicalimage data of the patient.
 14. The method of claim 1, whereincalculating fractional flow reserve (FFR) of the at least one stenosisregion using the simulated hyperemic blood flow and pressure comprises:calculating the FFR of the at least one stenosis region as a ratio of amean simulated hyperemic pressure distal to the at least one stenosisand a mean simulated hyperemic aortic pressure over a cardiac cycle. 15.An apparatus for non-invasive assessment of coronary artery stenosis,comprising: a processor; and a memory storing computer programinstructions, which when executed by the processor cause the processorto perform operations comprising: extracting patient-specific anatomicalmeasurements of the coronary arteries from medical image data of apatient acquired during a rest state; automatically detecting at leastone stenosis region in at least one coronary artery from the medicalimage data; calculating patient-specific rest state boundary conditionsof a model of coronary circulation representing the coronary arteriesusing the patient-specific anatomical measurements and non-invasiveclinical measurements of the patient at rest, wherein calculating thepatient-specific rest state boundary conditions comprises calculating aresting microvascular resistance at a termination of each of a pluralityof branches of the coronary arteries using the patient-specificanatomical measurements and the non-invasive clinical measurements ofthe patient at rest; calculating patient-specific hyperemic boundaryconditions of the model of coronary circulation using the rest boundaryconditions and a model for simulated hyperemia, wherein the model forsimulated hyperemia simulates hyperemia in the patient by changing onlythe resting microvascular resistance at a termination of each of aplurality of branches of the coronary arteries to a hyperemicmicrovascular resistance calculated as a function of the restingmicrovascular resistance at the termination of each of the plurality ofbranches without changing blood pressure or heart rate boundaryconditions, and wherein calculating the patient-specific hyperemicboundary conditions comprises calculating the hyperemic microvascularresistance at the termination of each of the plurality of branches usingthe calculated resting microvascular resistance by: calculating aresting average peak velocity as a function of a measured heart rate anda measured systolic blood pressure of the patient, calculating acoronary flow velocity reserve (CFVR) value for each branch of thecoronary arteries as a function of the resting average peak velocity andan age of the patient, calculating a patient-specific total coronaryresistance index (TCRI) as a function of the CFVR value and an estimatedresting mean arterial pressure (MAP), and calculating the hyperemicmicrovascular resistance at the termination of each of the plurality ofbranches as a function of the calculated resting microvascularresistance and the patient-specific TCRI; simulating hyperemic bloodflow and pressure across the at least one automatically detectedstenosis region of the at least one coronary artery using the model ofcoronary circulation and the patient-specific hyperemic boundaryconditions, wherein the model of coronary circulation comprises areduced order stenosis pressure drop model representing the at least onestenosis region and the reduced order stenosis pressure drop modelcalculates a pressure drop across the at least one stenosis region as asum of a viscous term, a turbulent term, and an inertance term:${{\Delta\; P_{s}} = {{\frac{\mu\; K_{v}}{2\;\pi\; r_{0}^{3}}q} + {\frac{\rho\; K_{t}}{2A_{0}^{2}}\left( {\frac{A_{0}}{A_{s}} - 1} \right)^{2}{q}q} + {\frac{\rho\; K_{u}L_{s}}{A_{0}}\frac{\partial q}{\partial t}}}},$where μ is blood viscosity, L_(s) is a length of the at least onestenosis region, q is a flow rate, A_(s) is a cross-sectional area ofthe at least one stenosis region, A₀ is a cross-sectional area of anon-stenosis region in the at least one coronary artery, ρ is a blooddensity, r₀ is a radius of the non-stenosis region in the at least onecoronary artery, and K_(v), K_(t) and K_(u) are viscous, turbulent, andinertance coefficients, respectively; and calculating fractional flowreserve (FFR) of the at least one stenosis region using the simulatedhyperemic blood flow and pressure.
 16. The apparatus of claim 15,wherein the coronary circulation model comprises one-dimensionalcomputational models representing the coronary arteries and aorta of thepatient.
 17. The apparatus of claim 15, wherein calculating the restingmicrovascular resistance at the termination of each of the plurality ofbranches using the patient-specific anatomical measurements and thenon-invasive clinical measurements of the patient at rest comprises:calculating the mean arterial pressure (MAP) as a function of themeasured heart rate, the measured systolic blood pressure, and ameasured diastolic blood pressure of the patient; calculating a restingmyocardial perfusion as a function of a rate-pressure product that is aproduct of the measured heart rate and the measured systolic bloodpressure of the patient; calculating a total resting coronary flow as afunction of the calculated resting myocardial perfusion and a mass of aleft ventricle of the patient; and calculating the resting microvascularresistance at the termination of each of the plurality of branches as afunction of the MAP and the total resting coronary flow.
 18. Anon-transitory computer readable medium storing computer programinstructions for non-invasive assessment of coronary artery stenosis,the computer program instructions when executed by a processor cause theprocessor to perform operations comprising: extracting patient-specificanatomical measurements of the coronary arteries from medical image dataof a patient acquired during a rest state; automatically detecting atleast one stenosis region in at least one coronary artery from themedical image data; calculating patient-specific rest state boundaryconditions of a model of coronary circulation representing the coronaryarteries using the patient-specific anatomical measurements andnon-invasive clinical measurements of the patient at rest, whereincalculating the patient-specific rest state boundary conditionscomprises calculating a resting microvascular resistance at atermination of each of a plurality of branches of the coronary arteriesusing the patient-specific anatomical measurements and the non-invasiveclinical measurements of the patient at rest; calculatingpatient-specific hyperemic boundary conditions of the model of coronarycirculation using the rest boundary conditions and a model for simulatedhyperemia, wherein the model for simulated hyperemia simulates hyperemiain the patient by changing only the resting microvascular resistance ata termination of each of a plurality of branches of the coronaryarteries to a hyperemic microvascular resistance calculated as afunction of the resting microvascular resistance at the termination ofeach of the plurality of branches without changing blood pressure orheart rate boundary conditions, and wherein calculating thepatient-specific hyperemic boundary conditions comprises calculating thehyperemic microvascular resistance at the termination of each of theplurality of branches using the calculated resting microvascularresistance by: calculating a resting average peak velocity as a functionof a measured heart rate and a measured systolic blood pressure of thepatient, calculating a coronary flow velocity reserve (CFVR) value foreach branch of the coronary arteries as a function of the restingaverage peak velocity and an age of the patient, calculating apatient-specific total coronary resistance index (TCRI) as a function ofthe CFVR value and an estimated resting mean arterial pressure (MAP),and calculating the hyperemic microvascular resistance at thetermination of each of the plurality of branches as a function of thecalculated resting microvascular resistance and the patient-specificTCRI; simulating hyperemic blood flow and pressure across the at leastone automatically detected stenosis region of the at least one coronaryartery using the model of coronary circulation and the patient-specifichyperemic boundary conditions, wherein the model of coronary circulationcomprises a reduced order stenosis pressure drop model representing theat least one stenosis region and the reduced order stenosis pressuredrop model calculates a pressure drop across the at least one stenosisregion as a sum of a viscous term, a turbulent term, and an inertanceterm:${{\Delta\; P_{s}} = {{\frac{\mu\; K_{v}}{2\;\pi\; r_{0}^{3}}q} + {\frac{\rho\; K_{t}}{2A_{0}^{2}}\left( {\frac{A_{0}}{A_{s}} - 1} \right)^{2}{q}q} + {\frac{\rho\; K_{u}L_{s}}{A_{0}}\frac{\partial q}{\partial t}}}},$where μ is blood viscosity, L_(s) is a length of the at least onestenosis region, q is a flow rate, A_(s) is a cross-sectional area ofthe at least one stenosis region, A₀ is a cross-sectional area of anon-stenosis region in the at least one coronary artery, ρ is a blooddensity, r₀ is a radius of the non-stenosis region in the at least onecoronary artery, and K_(v), K_(t) and K_(u) are viscous, turbulent, andinertance coefficients, respectively; and calculating fractional flowreserve (FFR) of the at least one stenosis region using the simulatedhyperemic blood flow and pressure.
 19. The non-transitory computerreadable medium of claim 18, wherein the coronary circulation modelcomprises one-dimensional computational models representing the coronaryarteries and aorta of the patient.
 20. The non-transitory computerreadable medium of claim 18, wherein calculating the restingmicrovascular resistance at the termination of each of the plurality ofbranches based on the patient-specific anatomical measurements and thenon-invasive clinical measurements of the patient at rest comprises:calculating the mean arterial pressure (MAP) as a function of themeasured heart rate, the measured systolic blood pressure, and ameasured diastolic blood pressure of the patient; calculating a restingmyocardial perfusion as a function of a rate-pressure product that is aproduct of the measured heart rate and the measured systolic bloodpressure of the patient; calculating a total resting coronary flow as afunction of the calculated resting myocardial perfusion and a mass of aleft ventricle of the patient; and calculating the resting microvascularresistance at the termination of each of the plurality of branches as afunction of the MAP and the total resting coronary flow.
 21. Thenon-transitory computer readable medium of claim 18, wherein calculatingfractional flow reserve (FFR) of the at least one stenosis region usingthe simulated hyperemic blood flow and pressure comprises: calculatingthe FFR of the at least one stenosis region as a ratio of a meansimulated hyperemic pressure distal to the at least one stenosis and amean simulated hyperemic aortic pressure over a cardiac cycle.